Problem: Ishaan is 4 times as old as Ben. Eight years ago, Ishaan was 6 times as old as Ben. How old is Ben now?
Solution: We can use the given information to write down two equations that describe the ages of Ishaan and Ben. Let Ishaan's current age be $i$ and Ben's current age be $b$ The information in the first sentence can be expressed in the following equation: $i = 4b$ Eight years ago, Ishaan was $i - 8$ years old, and Ben was $b - 8$ years old. The information in the second sentence can be expressed in the following equation: $i - 8 = 6(b - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to use our first equation for $i$ and substitute it into our second equation. Our first equation is: $i = 4b$ . Substituting this into our second equation, we get: $4b$ $-$ $8 = 6(b - 8)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $4 b - 8 = 6 b - 48$ Solving for $b$ , we get: $2 b = 40.$ $b = 20$.